Pattanaik’s axioms and the existence of winners preferred with probability at least half

• Autorzy: Lahiri Somdeb

Identyfikatory

DOI

10.37190/ord210205

• Języki publikacji: EN

Abstrakty

EN

We show that three conditions due to Pattanaik, when satisfied by a given profile of state-dependent preferences (linear orders) on a given and fixed set of alternatives and a probability distribution with which the various states of nature occur, are individually sufficient, for the non-emptiness of the set of alternative(s) which are individually preferred to all alternatives other than itself with probability at least half. Before this, we show that since each axiom individually implies Sen-coherence, then, as a consequence of a result obtained earlier, each axiom along with asymmetry of the preferred with at probability at least half relation implies the transitivity of the relation. All the sufficient conditions discussed here are required to apply at least to all those otherwise relevant events that have positive probability. This observation also applies to a sufficient condition for the non-emptiness of the set of alternative(s) which are individually preferred to all alternatives other than itself with probability at least half, called generalised Sen coherence introduced and discussed in earlier research.

Słowa kluczowe

EN

state-dependent preferences; preferred with probability at least half; fixed set of alternatives

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Operations Research and Decisions
• Rocznik: 2021
• Tom: Vol. 31, No. 2
• Strony: 109--122
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Lahiri Somdeb

• School of Petroleum Management, Pandit Deendayal Energy University, Gujarat 382426, India

Bibliografia

• [1] GILBOA I., Theory of Decision Making Under Uncertainty. Econometric Society Monograph, Cambridge University Press, New York 2009.
• [2] KARNI E., Decision Making Under Uncertainty. The Case of State-Dependent Preference, Harvard University Press, Harvard 1985.
• [3] LAHIRI S., Generalized Sen-coherence and existence of preferred with probability at least half winners, Int. J. Oper. Res., 2020, 17 (2), 93–99.
• [4] LAHIRI S., Extended choice correspondences. An ordinal framework for the analysis of choice under risk, 2020 (to be published).
• [5] PATTANAIK P.K., Sufficient conditions for the existence of a choice set under majority voting, Econometrica, 1970, 38 (1), 165–170.
• [6] RAIFFA H., Decision Analysis. Introductory Lectures on Choices Under Uncertainty, Addison-Wesley, Reading, MA, 1968.
• [7] RESNIK M.D., Choices. An Introduction to Decision Theory, University of Minnesota Press, Minneapolis 1987.
• [8] SEN A.K., A possibility theorem on majority decision, Econometrica, 1966, 34, 491–496.
• [9] SEN A.K., Collective choice and social welfare, Holden-Day, San Francisco 1970.
• [10] TAYLOR A.D., Mathematics and Politics. Strategy, Voting, Power and Proof, Springer-Verlag, New York 1995.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).